A tax is any fee levied by a government (excluding direct payments to the government for a service). Sometimes the tax is a fixed amount and sometimes it is calculated as a percentage of the value of the action. Examples of actions that are often taxed include earning income, buying cigarettes, buying anything, adding value to raw materials, owning a house or property, and occasionally dying.

Taxes are used by governments to generate revenue to support public services and as a tool of economic policy. Governments may both overtax or undertax their citizens. Arguably the Federal and state governments in the U.S. levy too little tax on motor fuel.[2]

Taxes are commonly used as an instrument of social policy. In the United States, renters are encouraged to become homeowners with mortgage tax credits. For decades, environmentalists have urged that tax credits be granted for investments in solar power, which would lead to less pollution and a decrease in dependence on imported fossil fuels.[3] More recently, a one cent tax on each e-mail was proposed as a way to eliminate virtually all spam, which may constitute more than three-fourths of all incoming e-mail messages.[4]

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There are generally three categories of taxation. For example, a progressive tax is a tax with the goal of shifting the tax incidence ("burden of taxation") onto those with a higher purchasing power, and away from those with a lower purchasing power. On the flipside, a regressive tax is a tax with the goal of shifting the tax incidence onto those with a lower purchasing power, and away from those with a higher purchasing power. In between, a proportional tax is a tax with the goal of the entire population carrying the same effective tax incidence.

To the layman, this may seem contradictory: how does a proportional tax achieve equal tax incidence? This misconception relies on a misunderstanding of the term tax incidence. When we look at the flat-rate tax, we expect to see it achieving that instead, after all, if everyone's paying, say, 20%, then the richer are paying more than the poor. Whilst this is true, it fails to account for the fact that the value of money for the poor is a lot higher than that of the rich due to a higher percentage of their money being allocated into needs rather than wants. Whereas the 20% taxed of the rich person will come out of a second home or third yacht, the 20% taxed of the poor person will come out of food and other such necessities.

Regressive taxes shift a heavy tax burden onto those with low income. A "tax per head" (or "poll tax"), when everyone pays the same amount (rather than the same percentage) is the most regressive tax possible, at least among those that are reasonably practical (it's possible to get more regressive by taxing the rich a lower amount than the poor, but that's very rare). If the income is equal to the poll tax, all of it is taxed, but there is 0% tax on income beyond that. A family can wind up in serious trouble if its income is less than the poll tax, for then the tax rate is over 100%. The poll tax was used in the middle ages in England to finance wars, and the burden it put on poor peasants and farmers was a major cause of the Peasants' Revolt in 1381. When the Iron Lady tried to implement it in the UK, widespread riots occurred that led her down the road to her own party kicking her out of power.

Estate taxes are levied on the wealth left behind by the deceased, usually with a relatively huge "deductible" to spare the middle class from them.

Poll taxes are fixed taxes (as opposed to taxes based on a portion of one's income). In some countries, notably the United States, the term applies to taxes that were historically tied to exercising the right to vote.

"User" taxes are fees charged for services nominally provided by government, in the case where the government can no longer afford to pay for the service.

Stupidity taxes are a fee charged people who are "on the internet being wrong" too often. The tax often takes the form of fees from service providers to cover the huge volume of traffic ("over 90 million pageviews!") caused by those who drop by to gawk at the stupidity.

A "Value Added Tax" (VAT) is charged to manufacturers and other processors on the difference between the cost of their raw materials and the resulting product.

is the required rate of return on equity, or cost of levered equity = unlevered equity + financing premium.

is the company cost of equity capital with no leverage (unlevered cost of equity, or return on assets with D/E = 0).

is the required rate of return on borrowings, or cost of debt.

is the debt-to-equity ratio.

is the tax rate.

Therefore, the higher the tax rate, the lower the effect of leverage has on the cost of equity. Assuming the unlevered cost is higher than debt,[5] higher taxes lead to an overall reduction of cost of capital. As such, values of investments made by the corporation can thus be computed at a lower required rate and have their net present value increased (so they can make more profitable investments).

For investment accounts that are taxable, which the losses are tax-deductible, the tax has an effect of reduction of risk through the following mechanism:

In case you make money, the taxable income is increased by the gain (net any legal deductions). This is called a capital gain in the U.S..

In case you lose money, the loss reduces your taxable income. This is called, as you might suspect, a capital loss. In the U.S., if an individual's capital losses exceed his capital gains during any tax year, he is only allowed to deduct up to $3000 of those losses (the rest get carried over into the next tax year).

As such, the magnitude of both gains and losses are reduced by the effective tax rate. This can be viewed as an reduction of risk (using most measurement that involves variation and magnitude of gains/losses).

Under U.S. law, if you sell an asset for more than you paid, less than 2 years after you bought it, it's a short term capital gain and is taxed at the same rate as ordinary income. If, however, you held onto it for 2 or more years before you sold it, the gain on the sale is a long term capital gain, and is taxed at a substantially lower rate (usually 15-20% in the uppermost income brackets). Investment companies typically make some ordinary income, some short-term capital gains, and some long-term capital gains every business quarter. They have the option of apportioning this money to their investors and their managers in any way they see fit, and more often than not they choose to earmark the long-term capital gains portion of this money to their managers' salaries and bonuses. This allows fund managers who make boatloads of money to be taxed at only 15-20% on this income, a fact that became a bone of contention during the 2012 U.S. Presidential Election.

If the interest expense on investment loans are tax-deductible, taxation can be seen as a device that encourages leverage, assuming the investor wants to keep the risk constant. Examples in U.S. tax law include the Home Mortgage Interest deduction, and (for low wage earners) the student loan interest deduction.

As far as an entity with control over the issuing and distribution of currency (i.e. monetary sovereignty) is concerned taxes are completely irrelevant to generating revenue. That is, government does not need your taxes to pay for things. An analogy might be helpful here: for a government without monetary sovereignty, if the shipment of tax money gets waylaid by Robin Hood, Nottingham can't fund the army because they cannot (or will not) create more money. For a government that does have it, when the supposed tax money gets carried off in Santa sacks by the Merry Men and destroyed in a battle by Guy of Gisbourne's troops Prince John can just shrug and print more money. There's no difference economically speaking between a government 'collecting' money then spending it and destroying the supposed tax money then issuing money.

So what are taxes used for in a Post-Keynesian world?

The first and most important is to generate a need to have the currency. If the government makes certain taxes mandatory and will only accept payment in this denomination, taxed individuals and entities will at least periodically need to hold certain amounts of it.

To destroy money in the case of runaway inflation.

Income redistribution to level the effects of income inequality. Redistribution is something of a misnomer since the government doesn't literally need another segment's money to give to another. Of course since people are sniveling and self-interested, PKs prefer to use inflation to accomplish the same thing to garner significantly less political resistance. Isn't omission bias just the cat's meow?[6]

As mentioned above, taxes are also used to regulate social and political activity.

Generally, countries only tax residents and don't tax nonresident citizens who live abroad, a practice called residence-based taxation. While many countries may still tax nonresident citizens on their domestic source income, or income earned at home, and residents on their foreign source income, income from foreign sources, they don't tax nonresident citizens on their foreign source income. There is one exception: the United States, which taxes all residents, but also taxes all U.S. citizens, green-card holders, and undefined "U.S. persons", who reside abroad on all their income. (Some also say that Eritrea is the one other example in the entire world, but this is disputed.) This unique policy is called citizenship-based taxation, and dates back to 1864, when during the Civil War they wanted to punish citizens who fled the country. In conjunction with recent attempts to force reporting on U.S. citizens by foreign financial institutions as part of the Foreign Account Tax Compliance Act (or FATCA, a pun on "fat cats"), there have been unintended consequences for ordinary U.S. expats who are now faced with onerous reporting requirements (for example, the IRS estimates it takes 15 8-hour days to complete one form),[7] even if they would not owe any tax, in the face of heavy penalties and fines for not reporting and for any mistakes, as well as banks and other foreign financial institutions refusing to let them, or their family members or business partners, open accounts, because the institutions find complying with FATCA to be too costly. However, there are other solutions to preventing tax dodging while not burdening nonresident citizens, which are practiced by other developed countries.[8]

↑Most of the time they are, otherwise they can simply lend money to obtain an arbitrage profit.

↑So you can either let the Great Satan of inflation (either directly or by funding programs that target the poor and middle class; the outcome is the same) reduce the relative holdings of the rich, take the rich's money out back and set it on fire to directly close the gap, or just stick your thumb up your ass and facilely moralize about benefit scroungers while income inequality eats away at your society like cancer-powered acid. Pick your poison, Austrians.